microstructure and molecular dynamics of elastomers as studied by

MICROSTRUCTURE AND MOLECULAR DYNAMICS OF ELASTOMERS AS

STUDIED BY ADVANCED LOW-RESOLUTION NUCLEAR MAGNETIC

RESONANCE METHODS

KAY SAALWACHTER*

INSTITUT FUR PHYSIK–NMR, MARTIN-LUTHER-UNIVERSITAT HALLE-WITTENBERG, BETTY-HEIMANN-STR. 7, D-06120

HALLE, GERMANY

RUBBER CHEMISTRY AND TECHNOLOGY, Vol. 85, No. 3, pp. 350–386 (2012)

ABSTRACT

Nuclear magnetic resonance (NMR) certainly belongs to the most powerful spectroscopic tools in rubber science. Yet

the often high level of experimental and in particular instrumental sophistication represents a barrier to its widespread use.

Recent advances in low-resolution, often low-field, proton NMR characterization methods of elastomeric materials are

reviewed. Chemical detail, as normally provided by chemical shifts in high-resolution NMR spectra, is often not needed

when just the (average) molecular motions of the rubber components are of interest. Knowledge of the molecular-level

dynamics enables the quantification and investigation of coexisting rigid and soft regions, as often found in filled elastomers,

and is further the basis of a detailed analysis of the local density of cross-links and the content of nonelastic material, all of

which sensitively affect the rheological behavior. In fact, specific static proton NMR spectroscopy techniques can be thought

of as molecular rheology, and they open new avenues toward the investigation of inhomogeneities in elastomers, the

knowledge of which is key to improving our theoretical understanding and creating new rational-design principles of novel

elastomeric materials. The methodological advances related to the possibility of studying not only the cross-link density on a

molecular scale but also its distribution and the option to quantitatively detect the fractions of polymer in different states of

molecular mobility and estimate the size and arrangement of such regions are illustrated with different examples from the

rubber field. This concerns, among others, the influence of the vulcanization system and the amount and type of filler particles

on the spatial (in)homogeneity of the cross-link density, the amount of nonelastic network defects, and the relevance of glassy

regions in filled elastomers. [doi:10.5254/rct.12.87991]

CONTENTS

I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351

II. Conceptual Basics and Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353

A. Basic Principles of Pulsed NMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353

B. Proton NMR and Mobility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355

C. Quantitative Detection of Immobilized Components . . . . . . . . . . . . . . . . . 358

D. Spin Diffusion Studies at Low Field . . . . . . . . . . . . . . . . . . . . . . . . . . . 358

E. Time-Domain Signals of Polymers Far above Tg . . . . . . . . . . . . . . . . . . . 361

F. MQ NMR Measurement of the Cross-link Density and Spatial Inhomogeneities 365

III. Recent Low-Field NMR Applications in Rubber Science . . . . . . . . . . . . . . . . 366

A. Are Cross-linked Rubbers Homogeneous or Inhomogeneous? . . . . . . . . . . 367

B. Quantitative Correlation of NMR and Equilibrium Swelling . . . . . . . . . . . 371

C. Filler Effects I: NMR-Detected Cross-link Density and Inhomogeneities versus

Macroscopic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

D. Filler Effects II: Surface-Immobilized Components . . . . . . . . . . . . . . . . . 376

IV. Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381

V. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382

VI. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383

*Corresponding author. Email: [email protected]; URL: www.physik.uni-halle.de/nmr

350

I. INTRODUCTION

This review is concerned with applications of modern low-resolution (LR) proton nuclear

magnetic resonance (NMR) techniques in rubber science. As we will see, a small set of robust and in

principle easy-to-use pulsed NMR experiments, implemented on simple and cost-efficient low-

field (LF) equipment, can be combined to reveal detailed information on inhomogeneities in rubber

materials. These comprise the quantitative assessment of not only the average cross-link density but

also its (spatial) distribution, the quantification of the amount of elastically inactive, no-load-

bearing polymer chains associated with connectivity defects or free chains, and the amount of

immobile polymer contributions, as for instance found as absorbed species on the surface of filler

particles or in the form of giant cross-links in thermoplastic elastomers or physical gels.

Rubbers are soft solids, and the elastically active polymer component, as discussed below,

features an almost liquidlike chain mobility. Nevertheless, the essential spectroscopic information

arises from a specific feature of solid-state NMR, namely, the orientation dependence of certain

magnetic interactions of the spin-carrying nuclei. The term spin interaction refers to corrections to

the Zeeman energy that is measured in NMR, such as the chemical shift, defining the exact position

of a spectral line or the through-bond isotropic J coupling between different nuclei, leading to small

splittings of the lines. The rather broad spectroscopic lines and thus bad resolution featured by

rubbers and even linear polymers in solution now arise from through-space dipole-dipole

couplings, which, owing to their orientation dependence (anisotropy), are usually averaged to zero

in low-molar liquids with isotropic mobility. However, residual dipolar couplings (RDCs) persist in

rubbery materials because the motion of network chains is anisotropic due to chemical cross-links

and physical entanglements.1 The RDC phenomenon is the reason for the low spectral resolution in

rubbers.

Therefore, solids-specific line-narrowing techniques such as magic-angle spinning (MAS) are

needed if rubbers are to be investigated with chemical detail. For principles and applications of

high-resolution solid-state NMR, the reader is referred to established monographs2–4 and review

articles,5–8 of which refs 5, 6 are specifically focused on solid-state NMR applications in the rubber

field. High-resolution NMR will not be further discussed in this article, yet its particular use should

be highlighted by the 13C MAS NMR studies of the chemical structure of cross-links in rubber by J.

L. Koenig and his coworkers,9–11 which can be considered groundbreaking. 1H MAS NMR, in

particular when applied under the conditions of very fast spinning, can further be used to detect and

characterize even small amounts of rigid filler-bound rubber components with chemical

resolution.12,13

The RDC phenomenon, which is directly related to the short transverse relaxation times (T2) of

rubbers measured in spin-echo experiments,1,14–17 is at the core of this article, as it provides an

indirect yet quantitative measure of the cross-link density. Similar studies have been carried out

using deuterium (2H) NMR, for which the quadrupolar coupling is the relevant anisotropic

interaction and which are based on much the same principles.18–20 However, such studies require

isotope labeling and the use of high-field instruments, stressing the practical advantages of proton

NMR. Apart from the quantitative study of cross-link density via proton RDCs, possibly in low-

field/low-resolution instruments21,22 or even in highly inhomogeneous fields of surface NMR

devices,23,24 it can be used as a contrast mechanism in NMR imaging experiments,25,26 whereby

inhomogeneities in cross-linking down to the 10 lm range are accessible. Below, we will deal with

the detection of inhomogeneities on even smaller scales. Anisotropic spin interactions further

reflect the mechanical stress at the chain level, which can thus be visualized in imaging experiments

on macroscopic, strained samples.27 NMR experiments on strained samples generally provide a

sensitive means to explore the validity of rubber elasticity theories,20,28 yet the large body of related

NMR work is beyond the scope of this application-oriented review.

MICROSTRUCTURE AND MOLECULAR DYNAMICS OF ELASTOMERS 351

In the following, an introduction into the underlying principles of the proton NMR response of

elastomers is presented, with an emphasis on observables that help explain the mechanical

properties of unfilled and, in particular, filled rubbers. Various low-field NMR applications will

then be presented, ranging from studies of model compounds that demonstrate the feasibility of

studying cross-linking inhomogeneities, comparisons of low-field NMR results with mechanical

and equilibrium swelling experiments, and finally a closer look at rubbers filled with a variety of

often nanometric particles.

Figure 1 highlights one of the intriguing features of filler effects in rubber. Although unfilled

SBR exhibits the expected positive temperature dependence as expected from the entropic models

of rubber elasticity in the high-temperature plateau region of G0, filled SBR has a much higher

modulus, which usually decreases significantly on heating. This is emphasized by plotting the

reinforcement factor30 R(DT)¼G0filled/G0

unfilled at a constant temperature difference to the glass

transition shown in the inset, which is seen to be highest at temperatures around and above the glass-

rubber transition. High values exceeding R¼ 10 and the decrease at higher temperatures indicate

synergistic and nontrivial effects of the filler network, where the NMR study of interfacial

phenomena in the as-made compound is of particular relevance, as a glassy layer of immobilized

polymer material on the particle surface may constitute the sticker between the particles, thus

explaining the softening at higher temperature.30

FIG. 1. — Sketch of the inhomogeneous nanoparticle distribution in a filled rubber for, for example, tire applications (upper

part) and storage modulus G0 in linear response at a shear frequency of 100 Hz of unfilled versus silica-filled SBR as a

function of temperature (lower part). The inset shows the reinforcement R¼G0filled/G0

unfilled as a function of temperature

difference to the glass transition. Tire image by courtesy of Continental AG; data from ref 29.

352 RUBBER CHEMISTRY AND TECHNOLOGY, Vol. 85, No. 3, pp. 350–386 (2012)

As we will see, low-field NMR techniques can be used to detect quantitatively the amount of

immobilized polymer in such filled systems and further to study, independently and specifically, the

cross-link density and potential inhomogeneities in the rubbery matrix of filled elastomers. In

particular, the latter two quantities are not directly accessible by any other comparably simple

technique but are of relevance for the understanding, modeling, and optimization of the mechanical

properties.

II. CONCEPTUAL BASICS AND EXPERIMENTS

This section gives an overview of the NMR concepts and experiments that are relevant for low-

field/low-resolution (LF/LR) studies of protons (1H), emphasizing the relevant observables, the

approaches for data treatment, and the relation of the results to molecular dynamics and structure in

rubbers. Importantly, LF/LR NMR implies that spectra are not of concern. The often valuable

chemical-shift information is always obscured by either the intrinsic signal width or (for the case of

mobile polymer components) magnetic-field inhomogeneity, as cost-efficient permanent magnets

are used. This means that the free-induction decay (FID), which is either directly acquired after the

common single 908 radiofrequency (rf ) pulse or after a more complicated pulse sequence, is usually

not Fourier transformed but rather analyzed directly in the time domain (TD). TD NMR and LF/LR

NMR are thus synonyms. Because the reader may be more familiar with NMR spectra than with TD

signals, some phenomena below will also be discussed in terms of their spectral features. Basic

knowledge of solution-state NMR is assumed, and the necessary background in pulsed solid-state

NMR is presented. Table I provides a list of the most relevant NMR experiments and concepts.

A. BASIC PRINCIPLES OF PULSED NMR

An LF TD NMR experiment in its simplest form consists of a single 908 rf pulse, with the rf

frequency tuned to the resonance condition for 1H nuclei in the given magnetic field. The rf

frequency corresponds to the Larmor frequency vL ¼ DE/h, where DE is the difference in the

Zeeman energy levels of the spin-up and spin-down states of a spin-1/2 nucleus in the primary

magnetic field B0. In LF NMR, magnetic fields are typically in the range of 0.2–1.5 T,

corresponding to vL of 10–60 MHz, which can be provided nowadays by permanent magnets. After

the 908 pulse has rotated the sample magnetization from jjz (along B0) to the transverse plane, the

magnetization vector starts to precess around the B0 field with the same vL, thus inducing an AC

voltage with the corresponding frequency in the same coil that was used for the pulse. Using clever

electronics, the very weak nuclear induction signal can be separated from the strong pulse (subject

to a so-called dead time problem, see below) and then amplified and digitized. This so-called FID

signal then persists for a time of a few tens of microseconds to many milliseconds, as limited by the

so-called apparent T2 relaxation time. Importantly, before digitization, the signal oscillating with n3 10 MHz is mixed down by subtraction of the vL carrier frequency (rotating frame), essentially

removing any oscillation if exactly the right frequency is subtracted (on-resonance FID).

In more complicated experiments, so-called pulse sequences consisting of one or many rf

pulses of variable duration and phase are applied either before or after the actual 908 pulse providing

the detected signal. The most simple of such experiments is certainly the popular Hahn-echo

experiment, where a 1808 pulse is applied after duration s after the 908 pulse. Signal acquisition then

starts another period s later on the top of an echo, in which effects of time evolution due to magnetic

field inhomogeneity are removed. In this way, true T2 relaxation times can be measured by

following the signal intensity in the TD as a function of s. Below, a number of more complicated

experiments based on the same principle (time variation in a complex pulse sequence, monitoring

changes in signal intensity) will be discussed.


TABLE I

EXPLANATIONS OF COMMON ABBREVIATIONS AND ACRONYMS OF VARIOUS NMR TECHNIQUES

Meaning Short explanation

HR NMR High-resolution

NMR

NMR at high (n 3 100 MHz) Larmor frequencies in very

homogeneous fields provided by superconducting magnets,

requiring specific line-narrowing techniques when solids are

investigated

LF NMR Low-field NMR NMR at Larmor frequencies of typically 50 MHz or less, often

provided by permanent magnets with high field

inhomogeneity, leading to low resolution

LR NMR Low-resolution

NMR

NMR in inhomogeneous, often low magnetic fields; spectral

features are blurred, chemical-shift resolution is lost

TD NMR Time-domain

NMR

NMR without Fourier transformation when it is not necessary

due to low resolution; analysis of time-dependent NMR

intensities rather than spectra, either directly on the detected

free-induction decay (FID) or as a function of a special

timing parameter in a pulse sequence, mainly to determine

relaxation times

MAS Magic-angle

spinning

Alternative to ‘‘static’’ NMR: fast (n kHz) rotation of the

sample in a ceramic tube inclined by 54.78 w/r/t the

magnetic field, leading to high-resolution solid-state spectra1H NMR Proton NMR NMR with protons as the most sensitive and most abundant

nucleus; in the solid state, the high abundance leads to

strong dipole-dipole couplings and bad spectral resolution13C NMR Carbon NMR Low natural isotopic abundance of 1% and low sensitivity

leads to low signal of this and other heteronuclei, requiring

signal enhancement techniques such as CP

CP Cross

polarization

Pulse technique used in solid-state NMR of 13C or other lowly

abundant, insensitive nuclei to enhance their low

polarization and thus increase the signal

MSE (Mixed) magic

sandwich echo

Special spin-echo pulse sequence leading to a time reversal of

all relevant spin interactions in static 1H NMR; used to

overcome the instrumental dead time and, with long echo

durations, as a dipolar filter in samples with regions of

different molecular mobility

MQ NMR Multiple-

quantum NMR

NMR based on pulse sequences creating special coherently

superposed states of many spins, mostly used in TD

experiments for the study of dipole-dipole couplings; can be

used to select and probe polymer regions of different

mobility on the basis of the different dipole-dipole couplings

DQ NMR Double-quantum

NMR

Special case of MQ NMR when only two spin pair interactions

are relevant


B. PROTON NMR AND MOBILITY

The only NMR fine structure effect relevant for 1H TD NMR is the distance-dependent

through-space homonuclear dipole-dipole coupling (DDC). In ordinary organic solids, the

coupling constant between neighboring protons is on the order of 20–30 kHz and thus dominates

the spectra even at the highest fields, leading to broad spectra with Gaussian shape. Because its

distance dependence follows~r�3, it is dominated by next-neighbor interactions, but because of the

high abundance of protons, it is nevertheless intrinsically a many-spin phenomenon. Because the

Fourier transform of a Gaussian function is again a Gaussian (with inverse width), the

corresponding TD signal is a half-Gaussian function with a decay time constant of typically 15–

20 ls.

The origin of the DDC interaction can be easily understood on the basis of two interacting bar

magnets representing magnetic dipoles with fixed orientation of their principal axes (corresponding

to the B0 field direction acting as quantization axis) and fixed distance of their centers. Obviously,

the potential energy of one magnet in the field of the other is changing its sign when the other magnet

is turned around by 1808. The magnets of course represent two spins, and the dipolar potential

energy is a small correction to the Zeeman energy. Because the spin-up and spin-down states are in

an ensemble almost equally populated, the resulting NMR spectrum shows a doublet for each

nucleus (or only one doublet if the two nuclei are magnetically equivalent), offset from the bare

Larmor resonance frequency by plus or minus the coupling constant.

The bar magnet analogy goes even further: even with fixed distance and fixed magnet

orientations, different configurations can be realized by rotating the intermagnet connection vector

relative to the fixed individual magnets’ orientations (identified with the external B0 field direction).

Such an overall rotation of the pair connection vector relative to B0, henceforth associated with the

angle h, changes the potential energy as well. The limiting cases for bar magnets are well-known,

that is, two bar magnets on top of each other with the same N/S orientation attract each other, but

they repel each other in side-by-side (h¼ 908) configuration. The dipolar splitting observed for a

single pair of equivalent nuclei is thus a function of orientation. Specifically, it follows the second

Legendre polynomial of cos h: P2(cos h)¼ 12(3 cos2h�1) The splitting for h¼ 908 (P2(cos 908)¼

�0.5) is thus half as large as for h¼08 (P2(cos 08)¼1); note that the sign change cannot be detected.

Because most NMR studies are performed on polycrystalline powders or amorphous substances, it

is clear that all possible orientations contribute to a given spectrum. For just spin pairs, this leads to

the characteristic double-horned ‘‘Pake’’ spectrum.31 Because protons are abundant, eachproton couples with many others (splitting of a splitting of a splitting . . . ), which leads to asmearing-out of the characteristic features and to the Gaussian spectral shape mentionedabove.

In the TD, the quick decay can be understood as an interference effect: the signal consists of

many differently oscillating components, each with its individual frequency because of the different

orientation-dependent couplings, which lose their phase relation. This process is termed dipolardephasing, and it is distinguished by the characteristic Gaussian shape as opposed to the common

exponential decay arising from motion-induced true relaxation effects. The difference between

coherent dephasing and true relaxation is that the former can be time reversed in a suitable spin-echo

experiment (see below).

The DDC discussed so far is thus an important measure of structure, as it reflects distance and

orientation of a pair of nuclei. More intriguing features come into play when the spins do not to stay

in place for the time scale of FID acquisition, which is on the order of the inverse width of the dipolar

spectrum. If molecular dynamics changes the spins’ orientation during this time, the appearance of

the spectrum (and the TD signal) changes. In the fast-motion limit, the spin pair changes its

orientation many times on this time scale. If all possible orientations are sampled, the static DDC


frequency is replaced by its time average, and because the average hP2ðcos hðtÞÞit ¼ 0 for dynamics

sampling an isotropic orientation distribution, dipolar broadening effects vanish in isotropic

liquids. This is the phenomenon of motional narrowing in the spectral domain and is highlighted in

the TD by FIDs of poly(styrene) shown in Figure 2a. It is seen that the action of DDCs, which are

responsible for the quick decay at low temperatures, vanishes upon heating above the glass

transition, when the monomer units start rotating almost isotropically (a process).

Motional narrowing of a spectrum is thus equivalent to an increase of the apparent T2 relaxation

(decay) time of the FIDs. The biggest changes occur around 419 K, which is about 35 K above the

glass transition temperature. This temperature may be tentatively called the NMR Tg. It is defined as

the temperature at which the correlation time of motion is on the order of the inverse DDC constant,

that is, in the microsecond range. NMR thus measures a high-frequency Tg in a similar sense as in

dielectric or mechanical spectroscopy. The width of a proton spectrum or, equivalently, the FID

decay time is thus a sensitive means to distinguish phase-separated polymer components by their

mobility, ranging from the rigid solid (tens of kHz line width, FID decays within ~50 ls) to the

isotropic liquid limit (<1 kHz line width, not resolved because of the field inhomogeneity, FID

decays on the many-milliseconds time scale).

Figure 2a also highlights two other experimental issues. First, the intensity of an NMR signal

follows the Curie law (~1/T), resulting from the decreasing thermal population difference of the

two spin states in the high-temperature approximation. Provided that experiments are conducted

with a sufficiently long relaxation delay (recycle delay�T1), the Curie law is followed exactly, and

a correction can easily be applied if needed. Second, the initial part of the FID is undetectable

because of the instrumental dead time, which is typically longer than 10 ls on LF instruments.

During this time, the strong rf pulse power is dissipated in the circuit, only then enabling the

acquisition of the much weaker NMR signal induced in the rf coil. Because theoretical predictions

of the signal shape are not generally possible or feasible, one cannot easily extrapolate the FID

signal to zero acquisition time (t¼0), which is an obstacle to a precise quantification of the NMR

signal (the signal at t¼0 is proportional to the total proton number in the sample).

This problem can be circumvented by applying a spin echo, which means that the FID decay is

time reversed, such that data acquisition can start at the top of an echo at effectively t¼0. At this

point, it is important to stress that the well-known Hahn echo (908� s/2�1808�s/2 � acq.) cannot

be used for this purpose, as it does not affect spin evolution because of homonuclear DDC. A solid

echo (using a 908 instead of a 1808 pulse) is a possible solution that has been frequently applied in

the filled-rubber context.32 However, for quantum-mechanical reasons, it is not very efficient, and

additional signal decay has to be corrected for by back-extrapolation over a series of echo delays s.

We have previously suggested the use of the more efficient so-called mixed magic sandwich echo

(MSE),33,34 which can also be easily implemented on LF equipment.35,36 The MSE is a complex

pulse sequence of duration 6s, which serves to refocus the time evolution due to both field

inhomogeneities (as does the Hahn echo) and multispin homonuclear DDC. The interval s is the

time between the last pulse in the sequence and the echo maximum, which must cover the dead time.

Figure 2b demonstrates the efficiency of this approach. Such MSE-FIDs are now amenable to

quantitative multicomponent fitting (see the next section).

A last point to comment on in this context is that the MSE is also not fully quantitative in

reconstructing the total magnetization (see Figure 2c). At very low temperatures (glassy range),

there is an ~20% signal loss associated with experimental limitations (finite minimum possible

pulse length), which can be easily corrected for. The more important effect is the intensity minimum

observed for temperatures around the NMR Tg. This is not only the temperature at which the

sensitivity of the TD signal to temperature changes is highest but also the temperature at which the

true T2 relaxation time during the MSE is shortest. Because the MSE is at least 60 ls long to

overcome the instrument dead time, the minimum true T2, which is on the order of 100–200 ls,


leads to another~30% signal loss at Tg þ 30–50 K. The condition for the T2 minimum is the same

as the one given for the NMR Tg: echo formation is impeded if the correlation time of motion is on

the order of the inverse NMR interaction (DDC) frequency. This is referred to as the intermediate

motional regime, and its effect on the MSE can, with some limitations, be used to study the time

scale of the a process.37,38

FIG. 2. — (a) FIDs of poly(styrene), PS, at different temperatures. The dashed lines are fits using a suitable theoretical

description. The decrease of the initial intensity with temperature reflects the Curie effect. Because of the finite receiver dead

time (rdt.), the initial 12 ls cannot be detected. (b) FIDs of another glassy polymer, poly(ethyl acrylate), PEA, in an

equivalent temperature range, detected after a magic-sandwich echo, which solves the dead-time problem. The solid lines are

again fits to theory. (c) Initial FID intensities taken from (b) and multiplied by T/(400 K) versus temperature. The intensity

minimum identifies the temperature at which the correlation time of motion is in the microsecond range. Data in (b) and (c) are

taken from ref 37.


C. QUANTITATIVE DETECTION OF IMMOBILIZED COMPONENTS

The sensitivity of the FID signal to motion can be used not only to study the molecular

dynamics of homopolymers at different temperatures but also, more importantly, to study

coexisting rigid and mobile components. A case specifically relevant to the rubber field is the

possible immobilization of the rubber phase by adsorption to the surface of filler particles. This

phenomenon will be discussed in more detail in the application section below. Our data for a model-

filled nanocomposite rubber system consisting of a cross-linked poly(ethyl acrylate) (PEA) matrix

and monodisperse ~30 nm silica particles shown in Figure 3 shall serve as an example.

TD signals of pure phases can in almost all relevant cases be fitted very satisfactorily with a

modified exponential function, ~expf�ðt=Tapp2 Þ

bg: For each component in an inhomogeneous

sample, one thus has three independent fit parameters: a fraction f, the apparent (!) relaxation time

Tapp2 ; and an exponent b. Compressed exponentials, also termed Weibullian functions, cover the

range from Gaussian (b¼2) to exponential (b¼1) decay, corresponding to temperatures below and

above the NMR Tg (see Figure 2a,b). Stretched exponentials (b< 1) indicate rather mobile phases,

combined with a distribution of decay times (inhomogeneous superposition of indistinguishable

but dynamically different components). Note that FID data should never be fitted for acquisition

times longer than 200–300 ls. First, the modified exponential function, as many other theoretical

functions like the ones calculated on the basis of the Anderson-Weiss approximation,39 is only an

approximation that works for sufficiently short times. Second, and much more problematically, the

shape of the FID on an LF instrument is generally ill-defined at long times because of the unknown

B0 field inhomogeneity.

The FID of the nanocomposite in Figure 3 clearly shows features of a rigid solid (signal decay

within~50 ls) on top of the signal of the pure matrix. In fact, a two-component fit is not sufficient;

thus, at least three components have to be used to obtain a satisfactory representation of the data.

These components can be associated with the rubber matrix, a phase of intermediate mobility closer

to the particles, and the rigid adsorption layer. In our work, we could show that this is only a minimal

model; in fact, the data are fully consistent with a region with a gradient in glass transition

temperatures, arising from the strong immobilization of the monomers in immediate contact with

the silica surface.37,40

This of course raises the question whether such decompositions are unique, considering the

many independent fit parameters. It must be stressed that fits with three or more components are

stable and make sense only if some of the fitting parameters can be determined independently and

thus be fixed during the fit. For example, the FID of the pure PEA matrix can, with some limitations,

be taken to represent the mobile phase in the nanocomposite. Suitable magnetization filters based on

pulse sequences that are sensitive to the different mobility (such as the MSE itself ) can further be

used to isolate the signal of only the mobile or only the rigid phase. Such strategies are discussed in

detail in refs 36 and 37. Another possible approach, applicable to systems with a smooth gradient in

mobility, is to find a suitable model that analytically describes this gradient and the corresponding

signal functions with only a few parameters and determine these from the fits.40

Similar strategies can of course be applied to study quantitatively the phase coexistence in

semicrystalline polymers35,41,42 or thermoplastic block copolymers consisting of hard and soft

blocks, such as SBS.36,43

D. SPIN DIFFUSION STUDIES AT LOW FIELD

The different NMR properties of phases with very different mobility can be used not only for

their quantification but also for the study of domain sizes, provided they are in the range of about 1–

100 nm. For this purpose, a quantum-mechanical process termed spin diffusion can be employed.


Spin diffusion arises from the exchange of the magnetization state of two neighboring spins (flip-

flop process) mediated by the DDC between them31 and becomes visible if regions in the sample,

such as different phases in an inhomogeneous system, can be selectively polarized.

In the ensemble average, a sequence of many such spin flip-flops leads to a time-dependent

magnetization profile that can be modeled as a diffusion process. Note that no actual material

transport is involved; the magnetization can diffuse among spatially fixed spins. Because estimates

and calibration procedures exist for the spin diffusion coefficient of many different glassy and

mobile polymers,4,44,45 spatial dimensions can be determined from the time dependence of the

overall magnetization in the different phases. The course of spin diffusion experiments is

schematically shown in Figure 4 for the cases of phase selection and distinction by chemical shift

(spectral, high-field only) and by mobility. The latter approach is relevant for LF TD NMR.

The basis of such experiments is the very same mobility-based magnetization filters mentioned

above. A spin diffusion experiment is nothing more than such a filtering pulse sequence, followed

by a spin diffusion period (mixing time, tm) during which the magnetization is stored along the z

axis and then read out by another 908 pulse, possibly using an MSE to detect a dead-time–free FID.

Typical data are shown in Figure 4c, where it is seen that the rigid-phase signal is gradually

reappearing in a time range of many milliseconds after it has been suppressed by a suitable filter.

The essential problem of such TD experiments at low field, as compared with high-field high-

resolution versions,4,46 is that T1 relaxation times of mobile components are particularly short at low

field, down to tens of milliseconds. In such cases, T1 relaxation competes with the spin diffusion

FIG. 3. — MSE-FIDs of cross-linked PEA, pure and filled with 20 vol-% of silica particles 27 nm in diameter, modified to

form chemical grafts to the rubber phase. The signal of the filled PEA can be fitted (solid line) and thus decomposed into three

components of different mobility (broken lines). Data taken from ref 37.


process, which is represented by the decay of the initial intensities upon increasing tm in Figure 4c.

Although component analysis is still straightforward, the analysis of the tm dependence of the

different signal fractions becomes rather involved if the extracted domain sizes should be more that

just rough estimates. This ultimately requires involved numerical simulation of the spin diffusion

data, which is the actual subject of ref 36. Even though we have tried to formulate some simple rules

for approximate data analysis along the lines of the established initial-slope analysis,4 currently

FIG. 4. — (a) Schematic illustration of the spin diffusion process after applying a magnetization selection in a

nanostructured, two-component inhomogeneous polymer sample, adapted from ref 44. (b) Spectroscopic observation of the

spin diffusion process after selection of one phase for cases in which the two components have a distinguishable chemical

shift. (c) Time-domain observation of the spin diffusion process after selection of the mobile phase for phases with largely

different mobility. Data taken from ref 37.


limited to lamellar morphologies, the truly quantitative evaluation of low-field spin diffusion data

involving components with short T1 cannot be considered routine at the moment.

E. TIME-DOMAIN SIGNALS OF POLYMERS FAR ABOVE TG

Let us now take a closer look at highly mobile components, defined by the condition that the

experimental temperature classifies as far above Tg, referring to the range in which the motional

narrowing effects on the FID are essentially complete and effects of the static DDC should be gone.

We thus deal with components whose apparent T2 relaxation time is on the order of or longer than

the short 200–300 ls range of the detected and fitted FID. To properly characterize the molecular

dynamics of such components, the B0 inhomogeneity effects have to be overcome, which is

traditionally done by taking a Hahn-echo decay curve, which is acquired by incrementing the echo

delay, and simply evaluating the intensity of the FID signal acquired at the echo top. The Hahn echo

time reverses and thus removes field inhomogeneity effects, and the resulting decay curve reflects

pure relaxation and, in fact, still some significant dipolar dephasing effects.

Figure 5a shows that the rotational dynamics of segments and thus the spin pairs within the

monomer units is anisotropic if the ends of a given network chain are fixed at the cross-link junctions.

This means that even when the motion is very fast, the average Sb ¼ hP2ðcos hðtÞÞit „ 0. Sb is the so-

called dynamic order parameter of the fluctuating chain, and it is directly proportional to a finite and

measurable residual dipolar coupling (RDC), characterized by an RDC constant Dres in units of rad/s

(D/2p is in Hz). Specifically,

Sb ¼Dres

ðDstat=kÞ ¼3

5N: ð1Þ

Dstat is the average static-limit DDC constant, and k is a correction factor<1 accounting for the spin

arrangement and motions within a statistical segment. N is the number of statistical segments of the

network chain, or, more precisely, the number of segments between topological constraints. The last

part of this relation was first calculated by Kuhn and Grun in the context of strain birefringence,47 and

the first NMR observations and theoretical explanations in polymer melts and elastomers are due to

due to Cohen-Addad1 and Gotlib et al.,14 respectively. In the former case, entanglements take the role

of the cross-links, and the associated reptation motion of long linear chains complicates the matter and

will not be discussed further (see refs 48 and 49 for details). Without entanglements, the first

appearance of a measurable Dres as a function cross-link formation between mobile chains is directly

related to the gel point.50

Equation 1 is the basis of the NMR determination of the cross-link density of rubbers, because

N�Mc; the molecular weight between cross-links. Because N is roughly of the order 100, Sb »0.01, this means that Dres is in the percentage range of Dstat. Note that entanglement effects also

contribute to Dres at moderate cross-link density, because more precisely Dres � (1/Mcþ 1/Me),

where Me is the entanglement molecular weight. There are numerous examples in the literature

addressing quantitative relationships between NMR observables reflecting RDC effects and the

cross-link density,15,17,51,52 many of them using LF/LR NMR.

The most important consequence of the presence of a small but finite DDC is that the transverse

relaxation (T2) decay is nonexponential. For homogeneous networks at high enough temperature,

the decay is in fact Gaussian, in perfect analogy with the rigid-solid case discussed in section IIB,

but of course on a roughly 100 times longer time scale (some milliseconds instead of tens of

microseconds):

Iecho ¼ exp9

40D2

ress2

� �ð2Þ


There is considerable disagreement in the literature as to whether Eq. 2 is correct or should be

modified in terms of models taking into account, for instance, a quasistatic Gaussian distribution of

end-to-end distances51 or effects of intermediate motions.16,53 As also discussed further below, our

work has evidenced that these effects never play an essential role at sufficiently high temperature

and that deviations of actual data from Eq. 2 are most often due to sample inhomogeneity.54–56

To reach the regime where the above function is applicable, the experimental temperature has

to be high enough to avoid a large additional influence of incoherent (true) T2 intermediate-regime

FIG. 5. — (a) The different lines signify snapshots, that is, possible conformational states of a given fluctuating network

chain. The orientational dynamics of a segmental vector b(t) (that can be associated with individual spin pair orientations) is

anisotropic in the long-time limit, characterized by a finite dynamic chain order parameter Sb. The associated order tensor

n� is oriented along the connecting line of the cross-links and is approximately the same for all monomers of a given chain. It

is of course isotropically distributed in an unstretched sample consisting of many chains. (b) Sketch of typical elastically

inactive, isotropically mobile components in networks.


relaxation processes, which lead to a faster decay and lend some exponential character to the

Gaussian dipolar dephasing. To check whether the regime of dominant RDC effects is reached, the

temperature should be raised until a T2 plateau is observed. An alternative to temperature change is

partial swelling52,57; the solvent then acts as plasticizer and speeds up the molecular dynamics. It is

often argued that working at moderate swelling degrees can help to remove entanglement effects

from Dres and thus quantify their relative contribution; however, one must keep in mind that Dres

changes rather nontrivially in swollen samples (see below and refs 58–60).

As mentioned, there are many reasons why a fit using Eq. 2 can be difficult. As is apparent from

the data in Figure 6a, there are often other, sometimes significant, signal contributions from

components with longer and almost exponential relaxation behavior. These can be associated with

network defects, solvent, or significant amounts of extender oil, which all move isotropically and

thus do not exhibit RDC effects but may differ in their T2 relaxation times. See Figure 5b for an

example of such elastically inactive components. The use of a two- or three-component fitting

function is thus advised, which can lead to ambiguous fitting results, in particular when the initial

decay due to the network component is not perfectly Gaussian. Apart from the mentioned

exponential relaxation contributions, network inhomogeneities, leading to a distribution in Dres and

a non-Gaussian signal decay, are a major reason for deviations from Eq. 2. See refs 54 and 61 for

discussions of possible artifacts in T2 relaxation studies of rubbers.

This is why the method of choice for a precision measurement of Dres ~ 1/Mc is multiple-

quantum (MQ) NMR, which can be straightforwardly implemented on LF equipment. The

technique has its predecessors in less robust combinations of solid and Hahn-echo signal

functions62–64 and was first applied to the study of order phenomena in linear polymer melts65 and

networks66 under high-resolution (MAS) conditions. Care has to be taken under such conditions,

as, for instance, the T2 relaxation times are strongly affected by MAS. Essentially, the RDC

effects are averaged out by MAS, and the T2 is not an easily interpretable quantity any more,

requiring the use of so-called recoupling pulse sequences to reintroduce the RDC and make it

measurable. This being not trivial, it was later realized that the static version of MQ NMR, first

applied to rubbers in ref 67 is in fact much more robust and can without any compromise in data

quality be carried out on LF equipment.21 A detailed account of the technique and many

applications in soft-matter science are reviewed by Saalwachter.22 The big advantage of this

method is that a largely temperature-independent response function (InDQ) can be generated that

is free of relaxation effects and that can be analyzed solely in terms of Dres (and distributions

thereof ). Sample data are shown in Figure 6b, and without any recourse to the somewhat involved

theoretical background, the discussion will focus only on some phenomenological aspects of data

acquisition and treatment.

The raw data comprise not one but two signal functions that are measured as a function of pulse

sequence duration sDQ. The DQ build-up function IDQ and the reference decay function Iref are

acquired with one and the same pulse sequence with slightly different internal settings (the phase

cycle differs). IDQ(sDQ) reflects Dres in its (inverted Gaussian) initial rise but is also subject to

incoherent relaxation effects at longer times. These can be removed by point-by-point division of a

relaxation-only function, the sum MQ decay IRMQðsDQÞ; leading the mentioned temperature-

independent normalized DQ build up InDQðsDQÞ: IRMQ is obtained from the sum of the two

experimental raw signal functions IDQ and Iref. It is in principle equivalent to an echo signal function

in which all coherent effects, DDC and shift/field inhomogeneity, are refocused.

Calculating IRMQ for the network component only is not straightforward because Iref contains,

in the same way as Iecho shown in Figure 6a, also the defect components, which need to be subtracted

before normalization. This subtraction procedure can be performed in a stepwise fashion, possibly

taking recourse to the artificially constructed data set Iref – IDQ, in which even signal tails can be


identified whose apparent T2 relaxation is almost the same as the one of the network component

itself. See Figure 6c for sample data and refs 22 and 68 for details.

MQ NMR is thus a more robust method than T2 relaxometry for the identification of signal

components and for the precise determination of Dres. The normalized InDQ build-up function

has a built-in quality control of the defect-fraction determination, as it must always reach an

intensity plateau of 0.5 in the long-time limit. An exception to such a favorable behavior are

inhomogeneous gels with components exhibiting largely different RDC and thus component-

FIG. 6. — Time-domain signals for cross-linked SBR with 80 phr silica measured at 80 8C, taken from refs 54, 68. (a) Hahn-

echo decay curves in semi-log representation, with lines indicating two exponentially relaxing defect fractions. (b) As-

measured (red up-triangles) and processed (black down-triangles) data from a multiple-quantum experiment. (c) Processing

involves a possible stepwise subtraction of defect components from Iref in semi-log representation, see text.


dependent and strong decay of IRMQ; see ref 69 for a discussion of possible data analysis

strategies.

F. MQ NMR MEASUREMENT OF THE CROSS-LINK DENSITY AND SPATIAL INHOMOGENEITIES

Fitting functions published in refs 22, 70, and 71 can be used for the analysis of InDQ, obtaining

a reliable average value for Dres. For a very homogeneous network (no Dres distribution), the generic

fitting function applicable to any simple polymer such as natural rubber (NR), butadiene rubber

(BR), poly(dimethyl siloxane) (PDMS), and the like, reads71

InDQðsDQ;DresÞ ¼ 0:5ð1� exp �ð0:378 DressDQÞ1:5f g3 cosð0:583 DressDQÞÞ:

ð3Þ

For inhomogeneous networks and rubbers based on copolymer chains or more complex monomers

(with dynamically decoupled side groups such as in alkyl acrylates), Dres distributions must be

taken into account, calling for multicomponent versions of Eq. 3. Conversion factors turning Dres

into cross-link density (~1/Mc) depend on the type of polymer and on the microstructure. Examples

were published and gauged against results from swelling experiments for the cases of NR, cis-BR,

and PDMS.70,72,73 An alternative is to use the linear relation between Dres and the shear modulus,74

using G0

» q R T=Mc ¼ m k T for calibration, as done in ref 29 and shown in Figure 7.

As noted, a key point of the MQ method is that the InDQ(sDQ) signal function can be reliably

analyzed in terms of distributions of Dres. This can be done by suitable fitting functions based on, for

example, a Gaussian distribution of RDCs.22 One then has the distribution width r (square-root of

the variance) as a second parameter characterizing network inhomogeneity. Alternatively, one can

use a numerical fitting procedure based on inversion of the distribution integral, which is related to

the inverse Laplace transform often used for the analysis of T2 relaxation data. Note, however, that

the latter is bound to fail in soft materials, because we have seen that T2 relaxation is intrinsically

nonexponential. Inverse Laplace transforms assume by definition a superposition of exponential

components and using it on intrinsically nonexponentially relaxing components can give

meaningless results. Our recent approach published in ref 71 involves the use of a reliable and

generic Kernel function in an algorithm based on Tikhonov regularization.75 The fitting program

and instructions are included in our publication71 as supporting information.

An experimental verification of the possibility to quantitatively characterize not only the

average cross-link density but also its local variations was earlier realized with bimodal model

networks.21,76 Such networks are made by end-linking of mixtures of long and very short telechelic

chains with four-functional cross-linkers. They are known to be phase-separated systems composed

of nanometer-sized clusters of short chains interconnected by long chains, as a result of mere

statistics, because the short chains always contribute the major fraction of cross-linkable ends.77

They represent an ideal test case for the ability of the MQ technique to detect an inhomogeneous

distribution of cross-link density in an elastomer.

Results from ref 76 are summarized in Figure 8. The bicomponent character of the build-up

curves in Figure 8a is clearly evidenced by the fact that the curves for the bimodal networks can be

modeled by mere superposition of the experimental curves for the pure-component networks,

weighted by their respective fractions. Actual fitting of such curves can be performed by using a

build-up function consisting of two components with different average Dres and variable

fraction.71,76 Alternatively, our Tikhonov regularization procedure yields an estimate for the actual

distribution function without assumptions on its shape. The corresponding results in Figure 8b

nicely demonstrate the two-component nature of these distributions for bimodal networks. Notably,

the position of the maximum of the more weakly ordered (less cross-linked) long-chain component

does not change appreciably by addition of short chains, indicating that these chains are not


hindered by the presence of the short ones. Such a dynamic decoupling of highly and lowly cross-

linked regions requires a spatial separation in the range of several nanometers. As explained in more

detail in the next section, directly connected short and long network chains (as present in

statistically cross-linked, i.e., vulcanized rubbers) show an averaged response and are not a priori

distinguishable by the technique.

III. RECENT LOW-FIELD NMR APPLICATIONS IN RUBBER SCIENCE

This section gives an account of recent TD NMR applications that are of direct relevance for

technical elastomers and rubbers, based on the principles and using the techniques presented in the

previous section. First, typical results for the NMR-determined cross-link density and its potential

inhomogeneity are presented for various elastomer types, also including the complex changes

occurring when swollen rubbers are investigated by NMR. A particularly useful approach is the

correlation of the cross-link density determined by NMR in dry samples with analogous results

from the popular equilibrium swelling (Flory-Rehner) experiments.78 These give valuable insights

into the quantitative character of the latter and also provide an interesting new means to study

interactions between the rubber matrix and filler particles. Results concerning filled elastomers also

comprise relations of the NMR results and mechanical properties and the relevance of surface-

immobilized rubber (glassy layers), for which very recent data and challenges are presented and

discussed.

FIG. 7. — Linear NMR-elasticity relation for sulfur–cross-linked SBR (21% styrene, 63% vinyl). The cross-link density v is

calculated from the plateau modulus in shear according to G0¼ vkT. Data taken from ref 29.


A. ARE CROSS-LINKED RUBBERS HOMOGENEOUS OR INHOMOGENEOUS?

NMR results for NR cross-linked with different cure systems79 are shown in Figure 9a,b. In

Figure 9a, the fraction of elastically inactive defects (see Figure 5b) is plotted versus the NMR-

detected cross-link density. For sulfur-based vulcanization, it is seen that the defect fraction decreases

strongly with increasing cross-link density, as expected from a random cross-linking process based

on long precursor chains, for which the defect fraction mainly consists of the progressively shorter

chain ends. In contrast, peroxide–cross-linked NR always contains between 20 and 25% defects,

indicating an important contribution of chain scission reactions. Similarly, high defect fractions are

more commonly observed only in networks based on shorter precursor chains, as recently studied in

detail for the case of PDMS.73 In this work, we found that the statistical treatment of Miller and

Macosko80,81 provides a precise quantitative prediction of the inelastic defects.

FIG. 8. — (a) Normalized DQ build-up curves for a series of bimodal end-linked PDMS model networks (Mc ¼ 41 and 0.8

kg/mol), with the weight fraction indicated. The dashed lines are not fits but merely linear combinations of interpolated pure

long- and short-chain network data in the known proportion. (b) Dres distributions obtained by numerical analysis of the nDQ

build-up curves in (a). Data taken from ref 76.


The Dres distributions in Figure 9b show that sulfur-vulcanized rubbers are highly

homogeneous, whereas peroxide-based cross-linking leads to substantial spatial inhomogeneity

in the cross-link density. The distribution component at higher Dres, related to highly cross-linked

regions, may arise from a secondary polymerization of double bonds in the unsaturated backbone,

leading to large multifunctional cross-links. An interesting correlation is presented in Figure 9c,

where the actual cross-link density (derived from the average Dres) is plotted versus the

FIG. 9. — (a) Fraction of nonelastic network defects in natural rubber samples vulcanized with two different sulfur-based

cure systems and dicumyl peroxide, measured at 80 8C and plotted versus the average NMR cross-link density (in terms of

Dres). (b) Representative cross-link density distributions for one sample from each series. The peroxide-based system is rather

inhomogeneous. (c) Efficiency of vulcanization as obtained by correlation of the cross-link density from NMR with

concentration of the vulcanizing agent. For sulfur-based systems, the slopes can be converted into the average length x of the

sulfur bridges. Data taken from ref 79.


concentration of the respective vulcanizing agent (sulfur or peroxide). The slope represents the

efficiency of the cross-linking process, and in the case of sulfur, the length of the –Sx– bridges can

be estimated. It is seen that the efficient vulcanization system (based on a larger concentration of an

amine accelerator) leads to significantly shorter bridges for both NR and BR.

It is further seen that peroxide-based cross-linking is much more efficient for BR than for NR.

This goes along with the observation that peroxide–cross-linked BR does not contain a large

fraction of defects, indicating that the mentioned chain-scission reactions are specific for NR,

possibly related to radical reactions that are influenced by its methyl group. However, it should be

mentioned that the peroxide–cross-linked rubber matrix is similarly inhomogeneous for BR as it is

for NR. A similar difference in matrix (in)homogeneity comparing sulfur- and peroxide-based

cross-linking was also evidenced for the case of EPDM-based rubber.82 Another recent MQ-NMR

study has evidenced a significant increase of the defect fraction, a decrease in the overall cross-link

density, and the appearance of network inhomogeneities upon thermal aging of nanoparticle-filled

EPDM.83 Maxwell and colleagues have early on observed similar thermal and radiation-induced

aging effects in different types of silicone elastomers (mainly PDMS) by T2 relaxation84 and later by

MQ NMR.84–87 It was generally found that aging leads to more defects and more inhomogeneities

but in this case to higher average cross-link densities.

Some basic considerations involving the in fact surprising finding of apparently very

homogeneous rubbers are summarized in Figure 10. Taking up Eq. 1, according to which Dres�1=Mc; we realize that Mc is in fact a distributed quantity; for instance, in a randomly cross-linked

rubber based on long precursor chains, a most-probable molecular weight distribution (Mw/Mn¼2)

is expected. In addition, the fixed-junction model also predicts a proportionality between Dres and

the squared end-to-end separation hr2i of the network chain, which again is a (Gaussian) distributed

quantity. The thus theoretically expected broad distributions of Dres are compared with a typical

experimental result in Figure 10a, and the question arises as to why effects of the undoubtedly

present distributions are not reflected in the data.56 It is important to note that the phenomenon of

narrow Dres distributions is also found in computer simulations of realistic, disordered networks.88

This issue, comparing and contrasting this surprising finding with earlier experimental and

theoretical results, is the subject of ref 56, in which we have proposed some preliminary

explanations. The efforts to completely understand this phenomenon are still ongoing, and with our

more recent work,60,73 the picture is getting clearer. More detailed analytical theory suggests that

the NMR-detected local order is proportional to the square of the force acting on the chain ends,60

and this force is of course balanced when short and long network chains, or chains with very

different instantaneous end-to-end separation, are connected. Such a force balance is possible only

if the cross-links are allowed to move, which is the essence of the phantom model of rubber

elasticity.89,90 The results presented below also corroborate that the phantom model provides a

more quantitative basis for the analysis of equilibrium swelling experiments than the affine fixed-

junction model.73,79 In summary, local force balances are probably responsible for the observation

of the uniform response of homogeneous (but still disordered) networks. An apparent exception

from this phenomenon are defect structures in swollen yet highly homogeneous model hydrogels

based on four-functional star precursors made from poly(ethylene oxide), PEO, in which well-

defined defect structures such as double-stranded links between two cross-links can be resolved

from the normal network chains.69

Generally, the RDC phenomenon has to be handled with care in swollen systems, as we could

experimentally show that networks deform highly nonaffinely (see Figure 10b,c and refs 59, 88).

These observations are again based on the fact that Dres � Sb � hr2i/N under ideal conditions (hsolvent, affine fixed-junction behavior). Experimental data are obviously at variance. In addition,

the phenomenon of swelling heterogeneities, well known from many scattering studies to occur in

the 100 nm range and above, is directly evidenced in the NMR data in Figure 10b. An important


complication is highlighted by the data in Figure 10c, where we see not only strongly subaffine

behavior but also that solvent quality (excluded-volume effect) rather than geometric effects (chain

stretching) alone plays a significant role.60 Therefore, MQ NMR experiments (and the less

quantitative but feasible T2 studies) should be performed on bulk samples or at small concentrations

in case some solvent is needed to speed up the chain dynamics and make the sample amenable to

NMR study.

FIG. 10. — (a) Apparent NMR cross-link density distribution (in terms of the backbone order parameter Sb, see Eq. 1), for a

sulfur-vulcanized NR sample, as compared to theory predictions assuming a Gaussian distribution of end-to-end distances of

the network chains and additionally chain length polydispersity. (b) Order parameter distributions of a PDMS end-linked

model network (linear precursor of 5.2 kDa) as a function of swelling degree Q¼V/V0 in octane below and at equilibrium. (c)

Change of the average RDC� Sb as a function of swelling for the same type of sample comparing good and h solvent. Data

taken from refs 56, 59, and 60, respectively.


B. QUANTITATIVE CORRELATION OF NMR AND EQUILIBRIUM SWELLING

The quantitative relationship between the NMR-detected average Dres and the network

structure has already been discussed in the context of Figure 7, where the linear relation with the

cross-link density derived from the plateau modulus determined by rheology or dynamic-

mechanical analysis was used for calibration. In Figure 11, analogous correlations between the

NMR-determined cross-link density and results from Flory-Rehner swelling experiments78 are

presented, as published in refs 72, 73. Again, we observe near-perfect linear dependencies. This

time, Dres was converted to actual cross-link density based on models of the spin dynamics within

the statistical segments of NR, cis-BR, and PDMS.70

We studied in detail the dependence of the results from swelling experiments on the way the

experiments are conducted and evaluated,72 addressing, for instance, the issue of defining proper

volume fractions in systems with fillers and significant amounts of other nonswellable components

such as ZnO. In particular, we addressed the differences arising from using Flory’s fixed-junction

affine versus James’s and Guth’s phantom model for the elastic contribution in the Flory-Rehner

treatment,78 where Figure 11a suggests a better mutual agreement with the latter. The consequences

of phantomlike behavior, which we have seen in the previous section to be physically reasonable

also from a chain dynamics point of view (force balance), have been addressed in another more

recent work focusing on PDMS networks.73 We in fact found that phantom behavior introduces a

dependence on the functionality of the cross-links not only into the final relation for the evaluation

of swelling experiments but also into the calibration relating cross-link density and Dres, here given

for the example of PDMS:

1

MPDMSc

¼ Dres=2p1266Hz

f

f � 2mol=kg: ð4Þ

This correction ultimately arises from the fact that the cross-link fluctuations can be treated in terms

of virtual chains, which effectively lengthen the actual network chains, leading to the factor of f/(f –

2).73,90 This affects both the evaluation of swelling and NMR experiments. The correction was not

yet part of the NMR-based data shown in Figure 11a,72 which means that the validity of the phantom

model actually cannot be inferred from these data, as the associated slope would result to be 2.52

instead of 1.26. However, in our recent work,73 we studied a large series of networks prepared under

very different conditions and used high-resolution 1H MAS NMR in combination with calculations

based on the Miller-Macosko theory of random cross-linking80 to obtain reliable absolute-value

results for the cross-link density as a gauge. In less highly cross-linked samples, the average

functionality of the cross-links was found to be significantly less than 4, and based on this variation

in f (which does not appear as a parameter in affine fixed-junction models), it is possible to

experimentally prove that the phantom description is qualitatively correct. As to absolute values,

the NMR results (Figure 11b, ordinate) are roughly a factor of 1.4 overestimated, whereas

equilibrium swelling results (abscissa, based on reasonable literature values for v) are

underestimated by about the same factor. These deviations are well within the model dependencies

underlying the NMR70 as well as the swelling experiments.

Deficiencies of the thermodynamic contribution to swelling equilibrium are in fact a significant

source of uncertainty. For instance, in our work, we referred the thermodynamic interaction

parameter v from the literature, where it is reported to be a function of solvent content and further to

be qualitatively different for solutions of linear chains and swollen networks.72 The basis of the

need for such ad hoc adjustments is certainly the simplistic nature of the Flory-Huggins treatment78

and possibly to some degree one of the basic assumptions of Flory-Rehner theory, according to

which elastic and thermodynamic contributions should be strictly separable. Although the use of

more realistic equation-of-state approaches is certainly advised, the Flory-Huggins treatment is at


present still the method of choice because of the large body of data in the literature for v of many

polymer-solvent pairs.

We finally comment on the apparent ordinate intercept that is visible in Figure 11, in particular

in part (a). This intercept is due to entanglement effects and does not appear in NMR-versus-

rheology correlations (Figure 7), as entanglements contribute equally to Dres and to the plateau

modulus. In swelling, however, entanglements contribute much less; their effect is reduced to

topologically active (‘‘trapped’’) links. This is why the intercept is found to be close to the

inverse entanglement molecular weight Me derived from the plateau modulus of an equivalent

linear-chain melt. The effect is much less pronounced for PDMS (Figure 11b) because of its higher

FIG. 11. — (a) Cross-link density m � 1/Mc of sulfur-vulcanized NR samples from NMR as compared with results from

equilibrium swelling based on Flory-Rehner theory78 using the affine and the phantom model. (b) The same for randomly

vinyl-functionalized PDMS networks vulcanized by a bifunctional linker, based on the phantom model and using Eq. 4,

taking account of the effective weight-averaged functionality of cross-links. Data taken from refs 72 and 73, respectively.


Me. It should be noted that the additivity concept ðDres�1=Mc þ 1=MeÞ holds only for small Mc. For

weakly cross-linked networks, a dominance of entanglement effects with Dres scaling as M�0:5e is

theoretically expected91 but cannot be observed because such long network chains have very long

relaxation times, violating the necessary prerequisite of fast-limit averaging on the time scale of the

experiment in the millisecond range.

C. FILLER EFFECTS I: NMR-DETECTED CROSS-LINK DENSITY AND INHOMOGENEITIES VERSUS

MACROSCOPIC PROPERTIES

Filler effects on various molecular parameters of the rubber matrix in which they are embedded

are frequently discussed and are of relevance for an in-depth understanding of the synergistic effects

of fillers on the material performance (see Figure 1). Often, such information is obtained indirectly,

either by performing solvent extraction experiments yielding the so-called bound rubber fraction, as

critically discussed in the next section, or by fitting theoretical models to rheological data, which

usually offer no option for an independent test of whether the resulting apparent changes in the

matrix cross-link density upon filling are true or not. This calls for a local, spectroscopic approach

that selectively probes the rubber phase, and TD NMR is here advocated as the most straightforward

choice.

Typical results from our work are presented in Figure 12. In Figure 12a, it is evidenced that

filling with both silica and carbon black (CB) has virtually no effect on the rubber matrix. Only a

slight shift of the cross-link density to lower values is seen, which is explained by inactivation of

parts of the vulcanization system by adsorption to the high-surface filler, leading to somewhat lower

cross-link densities. This effect can be significant, as demonstrated in Figure 12b in the example of

oil-extended SBR (thus containing 20% NMR-detected nonelastic components) filled with

increasing amounts of silica.29 Along with similar observations on a variety of other conventional

rubber-filler systems,92 we can conclude that filler effects on the matrix are usually rather minor,

which is at variance with a number of works based on indirect methods. It must be emphasized that

the NMR result is objective and model-free.

Figure 13 shows results for NR filled with clay minerals,92 which are a very promising new

class of nano-sized filler materials, as it is possible to obtain nanocomposites characterized by

almost perfect dispersions of molecularly thin (alumo)silicate sheets, which significantly enhance

the mechanical and barrier properties of rubber and many other commodity polymers already at

very low content.93,94 A good dispersion of the sheets is possible only if the clay is modified

beforehand by an organic surfactant, often an alkyl amine, which preswells the galleries between

the silicate sheets and enables efficient exfoliation upon processing. In Figure 13a, significant

changes of the NR matrix upon adding clay are evidenced; in particular, the exfoliated organoclay

sample exhibits a significantly increased cross-link density as compared with pure NR.

Looking closer, however, one realizes that the largest increase is found for a sample prepared

without clay but with the same amount of amine used to preswell the organoclay (NR-amine). Thus,

the increase is simply due to the amine acting as accelerator, rendering the vulcanization process

more efficient. There is no ‘‘nano’’ effect on the cross-link density; rather, each clay-filled

sample has a lower cross-link density than its appropriate counterpart. The correlation of the

average cross-link density fromNMRwith the plateaumodulus in Figure 13b is the expected

linear one, with the exception of NR-organoclay, which is obviously the only sample with

significant reinforcement related to a filler network. NR-clay is not exfoliated, and the low

level of filling (10 phr) does in this case not visibly enhance the mechanical properties. This

once again demonstrates the advantage of NMR as a local technique, allowing for a

separation of the effects that do or do not contribute to reinforcement. Weaker yet similar


effects were also found for the ternary system NR/clay/poly(ethylene glycol),95 in which thelatter aides in the exfoliation of the nanosheets.

In evaluating the possible contributions to reinforcement, the adhesion of the rubber matrix to

the filler surface is another important issue. For this purpose, correlations of the NMR-detected

cross-link density with results from equilibrium swelling turn out to be extremely useful (see Figure

14).92 In Figure 14a, all samples from the NR-clay series are shown to follow the same master line,

proving that the presence of filler does not affect the swelling process in any way. In such a case, the

network simply swells away from the filler, forming a solvent-filled bubble around the

nonswellable filler. The presence of this bubble can independently be proven by studying the

freezing point depression of the swelling solvent by differential scanning calorimetry (DSC).92

FIG. 12. — (a) NMR cross-link density distributions of pure and filled sulfur-vulcanized NR samples. (b) Average NMR

cross-link density (in terms of Dres), left ordinate, and defect content, right ordinate, of sulfur-vulcanized SBR samples

containing different amounts of silica. Data taken from refs 92 and 29, respectively.


In significant contrast, fillers with active surface modification, forming either chemical bonds

to the rubber matrix or at least offering adsorption sites that are stable against the competing solvent,

lead to lower degrees of swelling and thus to apparently enhanced cross-link density, which is

evidenced by a positive shift along the abscissa (Figure 14b). In such systems, the degree of

swelling can be expected to be inhomogeneous in the vicinity of the particles, which thus act as giant

nano- or even micron-sized cross-links.96 The most dramatic effect has been observed for samples

filled with functionalized graphene sheets (FGS), also referred to as thermally expanded graphite

oxide.97,98 This is another new, extremely promising filler system, leading to dramatic modification

of the material’s properties at extremely low levels of filling. In our case, this is evidenced by the

largest shift of the apparent cross-link density from swelling for a sample containing only 4% of

FGS. Note that the NMR-detected cross-link density as well as its distribution is again not

significantly affected, which proves that the average spatial distance between the stable adsorption

FIG. 13. — (a) NMR cross-link density distributions (in terms of Dres) of pure NR and samples filled with 10 phr

(organo)clay, also compared with a sample containing the same amount of amine used as organo-modifier. (b) Correlation of

the NMR cross-link density of the same samples with the plateau modulus. Data taken from ref 92.


sites of different NR chains on the FGS must be larger than or at least on the order of the distance

between cross-links. In other words, the NR adsorbed to FGS does not form a dense brush. In the

following section, it is demonstrated that filler-induced changes in the mobile rubber matrix can

indeed occur under such special circumstances.

D. FILLER EFFECTS II: SURFACE-IMMOBILIZED COMPONENTS

Figure 15 shows NMR-determined cross-link density distributions for an interesting class of

model-filled elastomers, based on an almost perfect dispersion of monodisperse silica spheres with

diameters in the 20–50 nm range in a matrix formed by PEA.30,37,99 The system is special in that the

FIG. 14. — (a) Correlation of cross-link density m � 1/Mc of sulfur-vulcanized pure and clay-filled NR samples (same

sample series as in Figure 13) determined by NMR and equilibrium swelling based on the phantom model. (b) Same type of

correlation for samples containing different types of fillers (surface-modified silica, carbon black, and functionalized graphene

sheets). The master curves (solid lines) are the ones from Figure 11a. Deviations from them prove strong (chemical and

absorptive) links exist between the filler and the matrix, thus restricting the swelling degree. Data taken from ref 92.


dispersion quality can be controlled by playing with the interparticle interactions in a colloidal

suspension of the particles in the monomer before cross-linking. The system can thus be tuned

between the limits of perfect dispersion and a high level of aggregation, where filler network effects

arise only in the latter case. See ref 100 for a review of the work related to these model

nanocomposites, which constitute a perfect model system for the study of rubber reinforcement

effects.

Two types of fillers are compared in Figure 15, namely, partially silanized silica spheres

exhibiting just absorption sites and spheres that are densely modified with a reactive linker forming

covalent bonds to the network matrix. It is seen that in the latter case, the matrix is indeed

significantly modified: the overall cross-link density is increased, and the apparent distribution is

broader, with indications for a bimodal behavior at high filler loadings. This phenomenon is

explained by the very high density of effective grafting sites.37 When the distance between such

constraints is much smaller than the average cross-link separation, the local order and thus the

molecular-level elastic response of the shorter network chains close to the particles can be expected

to be much increased.

It seems that the grafting densities that can be reached using CB or silica as fillers in

conventional rubbers are generally much lower, explaining the absence of comparable effects in

any of the conventional rubbers systems that we have investigated so far (e.g., Figure 12). Note that

silica fillers are usually used in combination with silanization agents that should provide chemical

bonds between the rubber and the filler; however, the grafting densities reached in this way are

apparently not very high. Another issue is the absence of filler aggregation in the presented system:

aggregation significantly lowers the internal surface area and thus the relative amount of surface-

modified polymer species.

FIG. 15. — NMR cross-link density distributions (in terms of Dres) of model-filled poly(ethyl acrylate) networks, comparing

samples filled with silica spheres just presenting absorption sites versus silica spheres with a high density of chemical grafts to

the network matrix. Data taken from ref 37.


The final issue to be covered in this review concerns polymer species in immediate contact with

the filler. Although the phenomenon discussed in the last paragraphs addresses topology effects on

still mobile (rubber elastic) chains, we now turn to species whose mobility is significantly reduced

as a result of strong adsorption interactions. The NMR response of such material, often referred to as

the glassy layer, is solidlike, and its quantification was discussed in the context of Figure 3. Results

of such component analyses for the case of the PEA-silica model nanocomposites introduced above

are compiled in Figure 16 and are the subject of ref 37.

The NMR signal (essentially simple FIDs) can be decomposed into three distinguishable

species, whose proton (¼volume) fraction is plotted as a function of temperature in Figure 16a. At

temperatures of about 60 K above the Tg of the PEA matrix, about 50% of all polymer in the given

(grafted) sample is found to exhibit a higher Tg. The interpretation in terms of an effectively

increased Tg is based on the finding that the immobilized polymer fractions decrease upon heating.

The high-temperature plateau value for this fraction corresponds to species with apparently infinite

Tg, that is, species that do not desorb below the sample decomposition temperature. More detailed

fitting of the NMR data, based on the temperature-dependent response of the pure matrix polymer

(Figure 2b) in combination with DSC results, showed that the phenomenon is fully consistent with a

smooth Tg gradient,40 for which the three-component fit is simply the minimal model that allows for

reliable fitting.

The total immmobilized polymer fraction for the given series of samples at a fixed temperature

(100 K above the matrix Tg) is plotted against the known specific inner surface in Figure 16b. It is

seen that very large ð� 20%Þ immobilized fractions are found only for the grafted samples, where

the chemical bonds between network and silica contribute to raising the effective Tg in the vicinity

of the particles. Nevertheless, the fraction is still substantial in the samples in which the PEA just

adsorbs to the partially hydrophilic silica, most probably by hydrogen bonds. From the known

geometry (perfectly dispersed spherical filler particles of known size), one can estimate the

thickness of the immobilized layer to about 5–6 nm for the grafted samples at 350 K. The high-

temperature plateau representing strongly adsorbed material in the nongrafted case is thus estimated

to be about 1–2 nm.

Complete immobilization leading to solidlike behavior mediated by hydrogen bonds is a well-

documented phenomenon that was first studied in detail for the system PDMS/silica.101–104 Even

though PDMS is generally a hydrophobic polymer, its Si-O-Si backbone is locally polar and can

form strong hydrogen bonds with a hydrophilic silica surface. Quantitative analyses of the proton

NMR response of systems with good dispersion and known particle size suggested a rigid layer

thickness of 1–2 nm,103,105 and the same is true for the system PEO/silica.106

If linear PMDS of sufficiently high molecular weight is blended with silica, one in fact obtains

permanent and even swellable elastomers,107–109 in which the strong surface adsorption withstands

the competition with an unpolar solvent. Using MQ NMR, we have studied the structure and

dynamic composition of such physical networks in which the silica particles thus form giant

physical cross-links.110 Similar phenomena are again observed for linear PEO/silica model

nanocomposites.106 Related phenomena are also responsible for the formation of physical gels

made of aqueous solutions of linear poly(vinyl alcohol) (PVA) subjected to freeze-thaw cycles. In

this special case, PVA crystallites form (the amount of which can be quantified by proton FID

decomposition) and act as giant solidlike cross-links connecting mobile, rubber-elastic chains

embedded in water as solvent.111

Immobilized surface-associated species are, however, an elusive phenomenon in conventional

filled rubber compounds. One of the earliest reports of small amounts of immobilized polymer

species in cis-BR/CB compounds, as identified by proton FID and T2 measurements, was by

McBrierty and coworkers.112 Fractions in the range of 10% or more in as-made composites have so

far been measured only in the mentioned model systems, whereas conventional filled rubber


compounds show immobilized fractions of less than 5% of the total rubber.113 In fact, our own work

has so far not indicated fractions in excess of 1–2% in NR or SBR systems at typical loadings,

irrespective of the filler type. Often, the immobilized fraction is virtually undetectable.

To better be able to study such species, it has become customary to subject unvulcanized

composite samples to a solvent extraction procedure. A gravimetric analysis of such samples gives

the so-called bound-rubber fraction, which represents a qualitative measure of the adsorption

capacity, related to the inner surface of the filler. As evidenced by proton NMR on such extracted

FIG. 16. — Results from FID component analysis (see Figure 3) in model-filled PEA networks, where significant amounts

of immobilized polymer are evidenced. (a) Signal fractions as a function of temperatures. (b) Total amount of immobilized

material as a function of inner silica surface for the two types of samples. The thickness of the layer at 350 K is estimated to

about 5–6 nm from the known filler size and total volume in the grafted samples. Data taken from ref 37.


samples, the bound-rubber fraction is in itself dynamically inhomogeneous and consists of

immobilized and still mobile networklike dangling and tie chains.32,113–116

The early work of Nomura and coworkers provided a first detailed picture of the changes of the

different bound-rubber fractions and their T2 relaxation behavior as a function of processing time of

NR/CB composites in a Brabender mixer.114 Legrand and colleagues115 pointed out the similarities of

CB- and silica-filled rubbers, where surface deactivation by grafting of alkyl chains was also studied

and shown to lead to lower amounts of highly immobilized species, in particular for silica. The very

detailed study of McBrierty and coworkers113 has revealed that solvent extraction of NR/CB

composites of increasing severity can yield compounds in which up to 35% of the polymer is

immobilized. Analyses of the signal components in EPDM/CB samples in combination with an in-

depth filler characterization, providing its inner surface area, have resulted in an estimated layer

thickness of, again, 1 nm.32 Based on the quantitative analysis of the T2 of the mobile networklike

component, Gronski and coworkers found for SBR/CB a typical mobile-layer thickness of 2–3 nm on

top of the immobilized layer.116 For all of the cited studies concerned with solvent-extracted samples,

it must be emphasized that the extraction procedure destroys the integrity of the filler network and may

further change the interfacial interactions substantially, putting into question the relevance of the so-

obtained results for explaining the reinforcement effects in actual rubber compounds.

Detecting and quantifying the potential glassy-layer material in as-used elastomers and

correlating it with the NMR-detected (true) cross-link density, the filler dispersion as obtained from

scattering experiments, and the linear and in particular nonlinear mechanical properties, is a promising

route toward a better understanding of reinforcement mechanisms. The presented model system based

on PEA/silica is particularly suited for this purpose, and significant progress has already been

achieved.30,99,100 According to our current understanding, the glassy layer acts in this case as a glue

holding together the filler network. Upon increasing the temperature, glassy bridges soften and the

reinforcement consequently decreases (see Figure 1). Long and colleagues have formulated a

mesoscale model based on the percolation of glassy bridges as one of the salient features of rubber

reinforcement, which in fact correctly reproduces the Payne and Mullins effects.117

This survey of current NMR results should be concluded with an open question concerning the

exact geometry of the glassy layer and the associated Tg gradient. As mentioned, the thickness of the

combined intermediate and glassy component layer in model composites of PEA with grafted silica

is about 5–6 nm at 350 K. This figure can be obtained from a simple volume consideration, as

mentioned above, and was also confirmed experimentally using spin diffusion experiments (see

Figure 4c for an example). The analysis of such data is so far based on rather approximate linear

extrapolation procedures, treating the system as consisting of two phases,36 combined immobilized

material versus mobile elastomer matrix.

Data from spin diffusion experiments on a PEA/silica model composite are presented in Figure

17. In the two plots, we see results from spin diffusion experiments, for which either the glassy layer

or the mobile matrix was used as a source of magnetization, using specific filters. In each plot, only

the time dependence of the sink phases is shown, this time considering three-component fits to the

signal functions. For the first case, it is seen that the magnetization first diffuses into the region with

intermediate mobility and then into the network matrix. The intensity decay at long times is due to

rather rapid T1 relaxation at low field. For the second case, the result is counterintuitive in that the

magnetization that starts in the network phase diffuses into the intermediate and into the glassy layer

with almost the same apparent rate.

This asymmetry calls into question the hypothetical picture of a smooth mobility gradient. As

mentioned, the analysis of such spin diffusion data at low field is so far not routine and requires

numerical modeling procedures.36 We are currently adapting our numerical procedures to other

possible geometries, and one scenario that could potentially explain the observed results is depicted

at the lower right of Figure 17. Probably, the assumption of smooth layering on a smooth surface is


simply unrealistic. The glassy layer may in itself be inhomogeneous, with changes in mobility not

only in the normal direction but also laterally. Also, a silica nanoparticle is not atomically smooth,

and once the surface roughness is on the order of the layer thickness, the immobilization of adsorbed

chains may also be influenced by the local curvature and the nanometer-scale confinement

geometry. We believe this observation to be quite general, as it is reproduced in other systems with

similar (alleged) mobility gradients, such as on the lamellar crystal surface in semicrystalline

polymers or at the domain interface in block copolymers consisting of hard and soft domains.

IV. SUMMARY AND CONCLUSIONS

The aim of this review was to familiarize the reader with the most important and current

concepts of proton low-field NMR as applied to the characterization of polymer materials,

with specific focus on rubber science. It was demonstrated how the fitting of simple time-

FIG. 17. — Results from TD spin diffusion experiments on one of the model-filled PEA samples, see also Figure 4. The

results for the glassy-layer–selected experiment exhibit the right order of magnetization flow, first into the intermediate

component and then into the network. The results for the mobile-phase–selected experiment are at variance and may be

explained by a nontrivial, disordered arrangement of glassy and intermediately mobile material, as sketched at the bottom

right. Unpublished data, courtesy of Kerstin Schaler.


domain free-induction decay signals, refocused by a suitable pulse sequence to overcome the

dead-time problem, can give reliable and quantitative information on the composition of

samples consisting of dynamically distinguished phases. Furthermore, the spin diffusion

effect can be used to estimate the size of the associated domains. The central phenomenon

concerning mobile chains far above the glass transition was the residual dipolar coupling of

mobile chains, which reflects the anisotropy of chain motion as arising from constraints such

as cross-links. As the most quantitative approach to study this phenomenon, multiple-

quantum NMR was discussed, which yields information on the cross-link density and its

spatial variations (i.e., cross-linking inhomogeneities).

Such molecular-level information on the microstructure of rubbers was shown to be

particularly useful when correlated with macroscopic material properties, such as the plateau

modulus or the cross-link density as derived from equilibrium swelling experiments. The

spectroscopic information obtained from NMR is local and thus unbiased, which means that effects

of nanoscopic filler materials on the rubber matrix can be studied objectively. One central result was

that most filler materials do not affect the cross-link density and the (in)homogeneity of the rubber

matrix very much, with the general exception of a slight decrease in cross-link density afforded by

partial deactivation of the vulcanization system by adsorption to the particle surfaces. An interesting

new perspective was opened by the correlation of cross-link densities determined by NMR and by

equilibrium swelling, through which active rubber-filler bonds are directly evidenced.

Using the sensitivity of proton NMR to mobility, it was shown to also be possible and

worthwhile to determine the amount of polymer that is immobilized by adsorption to filler particles

in as-made filled samples, where we put our focus on a special class of tunable nanocomposites

made from poly(ethyl acrylate) and monodisperse silica spheres. These materials show a

pronounced glassy shell, whose fraction depends on temperature in a well-defined way, suggesting

this class of materials as the perfect model to validate models explaining rubber reinforcement in

terms of glassy bridges between filler particles.

Although many of the cited NMR studies have revealed increasingly rich insights into

structural and dynamic aspects, in particular in filled elastomers, it is fair to state that a full

understanding of rubber reinforcement is still open. For instance, considering the rather low and

sometimes virtually absent signal contributions related to immobilized rubber, it is by no means

clear if glassy bridges are really a necessary prerequisite in any rubber compound for tire

applications or if they are only one part of the full and even more complex picture. Low-field NMR

studies will certainly continue to be useful in addressing these intriguing questions.

V. ACKNOWLEDGEMENTS

Funding of the work of the author presented in this review was mainly provided through

different programs of the Deutsche Forschungsgemeinschaft (DFG): SFB 418, SFB 428, SA 982/1,

SA 982/3, SA 982/6, and currently SFB/TRR 102. I also acknowledge funding from the Land

Sachsen-Anhalt, the Fonds der Chemischen Industrie, and infrastructural support from the

European Union (ERDF programme). The work presented herein would not have been possible

without the contributions of many coworkers and collaboration partners over the years, the names

of whom can be taken from the cited publications. I would specifically like to mention the

invaluable contributions of Jens-Uwe Sommer (Leibniz Institut fur Polymerforschung, Dresden) to

the theoretical interpretation of NMR observables in networks and Juan Lopez Valentın (ICTP-

CSIC, Madrid), who on his postdoctoral stay funded by the Humboldt Foundation masterminded

most of the projects focusing on current issues in rubber science and technology that are discussed

in this article.


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[Received February 2012, Revised February 2012]


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